In order to prove Theorem REF  we need to introduce the same distance relation which was used also by [1]}. Define for any two densities \(f_1,f_2\)  with respect to a measure \(\mu \)  on a space \(\mathcal {X}\)  and \(\alpha \ne 0\)  the distance relation
\(\rho _{\alpha }(f_1,f_2):=\frac{1}{\alpha }\int _{\mathcal {X}}f_1(x)\left(\left(\frac{f_1(x)}{f_2(x)}\right)^{\alpha }-1\right)d\mu (x).\) 
